The protostellar luminosity function ( PLF ) is the present-day luminosity function of the protostars in a region of star formation . It is determined using the protostellar mass function ( PMF ) in combination with a stellar evolutionary model that provides the luminosity as a function of instantaneous and final stellar mass . As in McKee & Offner ( 2010 ) , we consider three main accretion models : the Isothermal Sphere model , the Turbulent Core model , and an approximation of the Competitive Accretion model . We also consider the effect of an accretion rate that tapers off linearly in time and an accelerating star formation rate . For each model , we characterize the luminosity distribution using the mean , median , maximum , ratio of the median to the mean , standard deviation of the logarithm of the luminosity , and the fraction of very low luminosity objects . We compare the models with bolometric luminosities observed in local star forming regions and find that models with an approximately constant accretion time , such as the Turbulent Core and Competitive Accretion models , appear to agree better with observation than those with a constant accretion rate , such as the Isothermal Sphere model . We show that observations of the mean protostellar luminosity in these nearby regions of low-mass star formation suggest a mean star formation time of 0.3 \pm 0.1 Myr . Such a timescale , together with some accretion that occurs non-radiatively and some that occurs in high-accretion , episodic bursts , resolves the classical “ luminosity problem ” in low-mass star formation , in which observed protostellar luminosities are significantly less than predicted . An accelerating star formation rate is one possible way of reconciling the observed star formation time and mean luminosity . Future observations will place tighter constraints on the observed luminosities , star formation time , and episodic accretion , enabling better discrimination between star formation models and clarifying the influence of variable accretion on the PLF .